We consider the joint optimization of relay station (RS) placement and RS sleep/active probability in order to enhance the energy efficiency of a one-dimensional cellular network. When the RSs are always active, we derive the conditions for optimal RS placement that minimizes transmission power of base stations (BSs) and RSs, subject to a user rate requirement. The closed-form placement solution is obtained for a path-loss exponent of two, and a simple numerical method for the solution under general values of the path-loss exponent is proposed and evaluated. When the circuit power consumption of active RSs is considered, RSs should enter sleep mode to save power. To be tractable, and since the random user arrivals are not predicted by the network, we consider a basic scheme where each RS randomly switches between sleep and active modes with a certain probability. An algorithm based on the projected Newton method is proposed to jointly optimize the RS placement and active probability. It is shown via numerical examples that the benefit of implementing RSs and optimizing RS placement is substantial and increases with the path-loss exponent. We also demonstrate the interaction between RS placement and sleep control when the total power consumption, including both the transmission power and the circuit power, is minimized.